Professor: I thought we'd show examples based on a position Thomas emailed me earlier in the week.

Ryan: What kind of position?

Professor: You want to tell us about it Thomas?

Thomas: It’s a position with a queen facing off against a rook and knight.

Rachel: Any pawns?

Thomas: No pawns.

Hale: Can we see it?

Thomas: Sure.

Question 1: How can White force a win?

In no time, the class worked out the variation leading to a win.

Professor: So what can we say about this type of endgame?

Ryan: It seems the queen looks for a place to give a double attack.

Professor: I call such places “connection points.”

Rachel: Connection points?

Lucian: What’s a connection point?

Professor: A connection point is a square where a forking check is possible.

Rachel: I think it helps the queen if the rook and knight are not coordinating.

Hale: Then the queen can pick one of them off.

Thomas: It may help even more if the enemy forces are confined to the perimeter.

Lucian: Especially if there’s the possibility of mate in the air.

Professor: Good! Let’s look at another example.

Question 2: How can White force a win?

The class solved this one just as easily. Amid the din, there was commotion for more.

Idris: These first two positions were very similar.

Zephyr: Both times the black pieces were on the edge.

Lucian: At least in the second problem the black pieces weren’t in the corner.

Thomas: True, but it didn’t change things much.

Professor: Let’s see another problem.

Question 3: How does White force a win?

The group had no trouble solving this one. But it was Ryan, the second best player in the class, who got the right idea seconds before Idris.

Idris: Nice going, Ryan.

Ryan: Thank you, Idris. Coming from you, that means a great deal.

Idris smiled.

Professor: Shall we see another?

Question 4: How does White force a win?

There were some intricate variations, but after ten minutes, the key ideas had fallen into place. It was a true class effort.

Lucian: It's funny. It looked like White was going to win the rook at once.

Zephyr: Looks can be deceiving.

Hale: I had a feeling you might have an old saw to offer.

Professor: That’s enough of that. Let’s check out one more position.

Question 5: How does White force a win?

This proved more problematic. But impelled by Idris, the best player in the class, eventually the main branch of the win was worked out.

Ryan: Nice going, Idris.

Idris: Thank you, Ryan, but it was merely a simple matter of maneuvering the queen toward certain connection points, while avoiding any unpleasant surprises.

Zephyr: So that's what made it a simple matter.

Professor: Okay, Zephyr. Save your incisive wit for next week.

It was Zephyr’s turn to smile.

Professor: Well class, I hope you’ve enjoyed today’s offerings.

It seemed the class was silently indicating it had.

Professor: And thank you, Thomas, for providing a link to those curious problems.

Thomas: It was nothing. I was merely a connection point.

Answers below -- Try to solve NM Pandolfini's puzzles first!

Answer 1:

White takes advantage of Black's cornered forces and the queen's superior mobility. The winning line is 1. Qf7+ Kb6 (on 1...Ka6 White has 2. Qc7!, when 2...Kb5 fails to 3. Qb7+, with the square b7 being a connection point) 2. Qc7+ Ka6 (again, 2...Kb5 drops a rook to 3.Qb7+) 3. Kc5!, and Black is a goner.

Answer 2:

Here, Black's army isn't cornered, but the lack of mobility still hurts. After 1. Qe3+ Kf1 2. Kf4, essentially the same alignment is reached as in the first problem.

If Black continues 2...Kg2, White hits a connection point with 3. Qe2+.

So the knight must move. But after 2…Nb1, White wins with 3. Qf3+ Ke1 4. Ke3, and mate is in the air.

Answer 3:

Black's badly placed pieces, all on the h-file, are no match for White's tandem king-and-queen attack force. The winning line begins with 1. Qf5+.

Black has the initial threats. And 1. Qxa6 fails to 1…Rg1+. White must get the queen out of the corner, in quest of connection points.

The most concise winning variation, worked out by Rinck, is 1. Qd4! (a powerful queen centralization) Nb4 (it’s wise to bring the knight close to its own king for safety) 2. Qe3+ Ka4 (2...Kc4? results in 3. Qe4+, with e4 being a connection point) 3. Qa7+ Kb3 (3...Kb5 meets up with 4. Qb7+, with b7 being another connection point).

Finally, there’s a final connection point and the rook gets disconnected.

Take note:

In comparable situations, a practical way to start your analysis is by asking a simple question: where are the connection points? This query may not unearth all the vital information, but it should provide some help in getting your thinking off the ground, while keeping you more focused.